Professor, Physics Division, VIT-Chennai
Compton shift
derivation:
Compton wanted to study the scattering phenomena of X-rays with
a Carbon target. The schematic diagram of his experimental setup
is as shown in the following figure.
To clearly demonstrate the shift in the wavelength of the X-rays, he
has chosen monochromatic X-rays. Collimators are used to focus
the X-rays finely.
X-ray spectrometer is used to detect the scattered X-rays.
, Spectrometer is planned to travel through a circular track, so as to
receive scattered X-rays from φ=0° (for X-rays which are
penetrating through the target) to φ=180°. Engineering Physics - PHY 1001;
N. Punithavelan, Assistant Professor, Physics Division, VIT- Chennai
Engineering Physics - PHY 1701; N. Punithavelan, Assistant
Professor, Physics Division, VIT-Chennai
Here X-rays photons energy could be chosen in such a way that
electrons will not be ejected outside the carbon atoms. The
electrons are just recoiled (sprang back) due to the collision of the
X-ray photons. Thus x-ray photons are scattered by the electrons.
Compton’s experimental results are as shown in the figure. If
photons were behaved only as waves there should not be any new
waves with new wavelength as shown for scattering angles φ=45°,
φ=90°, φ=90° and φ=135°. The additional waves with wavelengths
are due to the particle nature of the X-rays.
Compton mathematically estimated the shift in the wavelength of
the X-rays by using the laws of conservation of energy and
momentum of X- ray photons and electrons.